Palm Trees in Hawaii with the sunset behind them are one of the most beautiful things and are harder to capture than one would think.
The Polynesian Cultural Center is a very interesting. It is a very educational and fun thing to do while on Oahu.
Ho'omaluhia Botanical Garden
Ho'omaluhia Botanical Garden, which has no admission fee, is a nice escape from the hustle and bustle of Honolulu and Waikiki. If you are lucky you might even get to see a wild boar or four. There are many trails to wander around on.
Peal Harbor is of course one of the most famous places on the island. Their are free as well as paid part of the monument. It is worth a visit.
Waimea Falls is one of the many falls which can be found on the island. If you go to Waimea Falls near dusk in December remember to put on the bug spray!
Tropical flowers abound on the island in so many shapes and sizes. Make sure to get a whiff of some of the highly scented varieties to fully immerse in the tropical feel.